in the parallelogram shown, ae = p - 8, ce = 2p - 58, and de = p + 15. what is the length of line segment…
in the parallelogram shown, ae = p - 8, ce = 2p - 58, and de = p + 15. what is the length of line segment eb? 42 units 50 units 65 units 73 units
Answer
Explanation:
Step1: Use parallelogram property
In a parallelogram, the diagonals bisect each other. So (AE = CE). Set up the equation (p - 8=2p - 58).
Step2: Solve for (p)
Subtract (p) from both sides: (- 8=p - 58). Then add 58 to both sides: (p=50).
Step3: Find (DE)
Substitute (p = 50) into the expression for (DE), (DE=p + 15). So (DE=50+15=65).
Step4: Use diagonal - bisecting property again
Since the diagonals of a parallelogram bisect each other, (DE = EB). So (EB = 65).
Answer:
65 units